Question

The bases of an isosceles trapezoid are represented by 3x and (3x + 4). The height of the trapezoid is represented by (x + 2). Which polynomial expression BEST represents the area of the trapezoid?

Answer 1

A)
`3x^(2) +8x+4`

Explanation:

Answer 2

The polynomial expression represents the area of the trapezoid is:

`Area = 3x^2 + 8x + 4`

Solution:

Given that,

The bases of an isosceles trapezoid are represented by 3x and (3x + 4)

The height of the trapezoid is represented by (x + 2)

To find: area of the trapezoid

The area of the trapezoid is given as:

`Area = (1)/(2) (b_1 + b_2 ) * h`

Where b₁ and b₂ are the bases and h is the height

Therefore,

`Area = (1)/(2) (3x + 3x + 4) * (x + 2)\\\\Area = (1)/(2) (6x + 4) * (x + 2)\\\\Area = (3x + 2)(x + 2)\\\\Simplify\\\\Area = 3x^2 + 6x + 2x + 4\\\\Area = 3x^2 + 8x + 4`

Thus the polynomial expression represents the area of the trapezoid is found